A pressure sensor device having a pressure detection module is described in German Patent Application No. DE 102 28 000 A1. The pressure sensor device described therein is situated in a housing and uses a pressure sensor, in particular a semiconductor pressure sensor, to detect the pressure. This sensor has a sensor diaphragm, which is provided on the upper side with sensing elements, the central section being spanned on the upper side by the sensor diaphragm. The pressure is supplied to the sensor diaphragm through a recess introduced into the rear side of the semiconductor pressure sensor, which is manufactured by reactive ion etching, for example. The semiconductor pressure sensor is soldered with its recess above a pressure channel of a housing part in such a way that the pressure channel and the recess have a direct pressure connection. The sensing elements on the upper side of the semiconductor pressure sensor generate electrical signals upon the application of pressure, which are relayed via electrical connections (for example, bond wires) to a carrier substrate or directly to contact elements. A cover part closes the pressure sensor device. To determine an absolute pressure with low measuring tolerances with the aid of such a pressure sensor device, it is necessary to maintain a constant pressure, ideally a vacuum, a so-called reference vacuum, in the housing on the non-pressurized side of the semiconductor pressure sensor. Therefore, the electrical signals are conducted outward through hermetically sealed, for example, glazed, contact elements. Manufacturing such a pressure sensor device having a reference vacuum in the housing and implementing the hermetically sealed contact elements requires a comparatively large structural volume of the pressure sensor device; in addition, the manufacturing is complex and the hermetic sealing of the contact elements is linked to high costs.